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Heuristic-Based Optimization Models for Assembly Line Balancing

in Garment Industry

Natayanee KETMATEEKAROON Jaramporn HASSAMONTR

Department of Production Engineering,King Mongkut Institute of Technology North Bangkok,

1518 Pibulsongkram Rd., Bangsue, Bangkok, 10800 Thailand tel. 66-02-913-2500, fax 66-02-587-0029

Abstract.

While assembly line balancing problem has been investigated by researchers for decades, its

solution techniques have been used sparingly in practice. In garment industry, for example, the number of

workers, their skills and the number of operations and their constraints involved often lead to too large integer

linear programming models to solve by a commercial ILP solver. In this research, a heuristic method is

developed based on greedy strategy to solve the assembly line balancing problem where there is more than

one machine per station and there may be parallel stations. The method is directly implemented on a

commercial ILP solver. Case studies from a nylon bag manufacturing company are used to illustrate its

capabilities. The parameters influencing line balancing performance, such as target cycle time, the number

of workers and parallel station decision criteria are investigated and discussed. The method is currently

tested by the nylon bag manufacturing company to perform line balancing for a team of workers.

1. Introduction

Garment industry is a very labor-intensive industry. Its productivity is predominantly driven by workers'

sewing skills. Typically it takes 1-2 months to train a worker extensively from not knowing anything about

sewing to the level that he/she can work efficiently in the production line. Unfortunately very few companies

are able to afford such training in practice. Instead they employ on-the-job training approach and have sewing

supervisor teaches necessary skills to new workers. Consequently, workers are trained by performing the

operations on a large number of actual workpieces. The sewing supervisor is usually the one to assign

operations to workers so as to balance the overall line cycle time. As the industry now moves toward

fashionable products, it must adjust their operations to work on much smaller lot sizes. This unavoidably leads

to shorter preparation time for each production lot. This research focuses on developing a practical

methodology to assist sewing supervisor perform effective line balancing.

In garment industry a product is manufactured through a series of operations. Each operation must be

performed on a machine(sewing machine) with a specific machine setting, i.e. yarn color, machine

attachment. Manufacturing a product always requires different types of sewing machines and different yarn

colors, making it difficult to assign a worker to perform operations on just a single machine. There is a

maximum number of machines that each worker can use for a particular product. Figure 1, for examle,

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denotes the line configuration of the problem considered in this research of which each worker can use at

most three different machines. For the ease of working, identical machines of different settings will be treated

as different machines. The worker therefore needs not to adjust the setting every time he/she performs an

operation.

The decision making scheme developed in this research is to assign operations and their

corresponding machines to a team of workers so that the line cycle time is minimized. The optimization model

takes into account workers skill levels as well as the constraint on the number of machines at each

station(worker). Each operation can be classified as a skill type. Each worker in the team is evaluated for all

these skills on standardized tests. The ratings based on time required to perform such skill to meet acceptable

quality level is given to each worker for each skill. This rating system allows for incompetent workers who

cannot perform certain skills as well. The solution approach is divided into two phases. In the first phase, a

multi-stage integer programming model is developed to assign operations, corresponding machines and their

settings to stations considering standard operation times, station by station. Parallel stations are allowed so as

to improve overall line cycle to as well as to use the required number of workers. Then in the second phase,

another integer programming model is used to assign workers to stations based on their aptitudes to minimize

the overall line cycle time.

Fig. 1. Assembly line consists of a team of workers performing tasks. Each task must be performed using

operators skill and a machine

Both phases are implemented on a spreadsheet software interfacing with a commercial integer

programming solver software , LINGO. Case studies are used to illustrate the proposed solution procedures

capability. The effects of parallel station criteria and the number of workers on line balancing performance are

discussed. It is currently used by a company manufacturing nylon bags.

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2. Literature Review

Assembly line balancing problems have been investigated by researchers well over 4 decades. The

problem was first introduced as an integer programming problem. [1] and [3] had proposed well-known

heuristic methods to group operations into stations. The linear programming model was introduced by [2]. The

dynamic programming formulation for assembly line balancing problems was proposed and solved by [4]. [5]

proposed the formulation in zero-one integer programming and solved the problem using Fibonacci search.

An improvement on branch-and-bound method to solve the assembly line balancing can be found in [6]. [8]

applied a backtracking technique to the network precedence diagram.

Several researchers investigated the problems of assembly line design. [16] and [17] provided good

general overview on the topic. [13] focused on designing assembly line for modular products. While much

work has been done in solving the assembly line balancing problem effectively, the techniques are difficult to

apply in practice. For example, the number of workers available must be taken into account in the assembly

line balancing. [7] and [12] addressed the issues of assigning more than one worker to the station. [11]

considered the problem of assigning tasks to a fixed number of stations using assembly line mapping

techniques. [9] and [14] also tried to determine the minimum number of workers for the assembly line.

Other aspects in assembly line balancing research include stochastic task times as considered by [15].

The actual applications of assembly line balancing have been limited, except in automotive industry. [10]

reported an interesting application of line balancing in home appliance manufacturing. In the paper, several

aspects not generally considered in research community were addressed. For example, some of the tasks are

considered float. They can be assigned to certain fixed tasks only. Some tasks may be incompatible with other

tasks as well. The work presented in this paper is along the same line as the work in [10] in that it focuses on

machine or tooling restrictions. It is, however, inspired by the sewing operations in nylon bag manufacturing

industry where human workers skill plays an important role in determining the operation time. Furthermore, the

number of workers to be used is fixed.

3. Problem Formulation

Similar to garment industry, bags are made by sewing operations. However, the sewing operations for

nylon bags require several types of sewing machines, making the skill required to perform individual operation

varies. The following are assumptions associated with the problem formulation considered in this research.

Skills to perform an operation can be classified into a limited number of categories. For example, in the

case study considered, there are 49 skill types. A operation is classified as one skill type only.

Operator's aptitude toward each skill is evaluated and known in advance. There are 4 levels of skill

aptitude. An operator receives anA rating for a skill if he/she can complete standardized task of that skill

with at least 20% faster than the specified standard time. The B rating is given to an operator who can

complete the task of that skill within 20% of the standard time. The Crating is given to an operator who

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takes at least 20% longer than the standard time to complete the task of that particular skill. If the worker

cannot or never perform the task of that particular skill, a zero rating will be given. In practice, such zero

rating implies that the worker may receive on-the-job training to perform the task and, therefore, takes

significantly longer time than the C-rating worker. In this research, it is assumed that the zero rating

implies that the worker takes twice as long as the standard time to complete the task.

There are several types of sewing machines. In the case considered, there are 6 types, each will have

only one setting. For the sewing machine, the setting represents yarn colors, attachment for the sewing

task. A typical product would have about three different yarn colors. Thus, with the combination of both

sewing machines and yarn color, there will be up to 18 different kinds of machines. Machine 1 is of type 1

with color setting 1, machine 2 of type 1 with color setting 2, machine 3 of type 1 with color setting 3, and

so on.

Each operator can use at most three machines in a station. This constraint is due to the U-shaped lineconfiguration as shown in Fig.1.

Target cycle time, Tc, is pre-specified.

All product information, such as operation details, its corresponding skill type, standard time, required

machine and immediately preceding operations, is given.

The formulation of assembly line balancing problem can be explained as follows. First, the time required

by each worker to perform each operation is estimated deterministically. Let gik

be an aptitude rating of worker

ion skill kand fjk

a binary parameter to indicate whether operationjis designated as skill type k. Note that the

summation of fik

for all k's would be unity since each operation can be classified by one skill type only. The

time factor for workerito perform skill k, hik, can be calculated from

=

=

=

=

=

0if2

if21

if1

if80

ik

ik

ik

ik

ik

g

Cg.

Bg

Ag.

h . (1)

Then the estimated time for workerito perform operationj, tij, can be calculated from

=k jkikjij

fhwt , (2)

where wj

is the standard time to perform operationj.

The assembly line balancing considered here is more complicated than those discussed in the

literature since more decision variables are necessary to ensure that constraints on workers and machines are

met. Fig. 2 defines all binary decision variables necessary. For example, binary variables xij

are to indicate

whether workeriis assigned to perform operationj.yjm

and zms

are defined similarly. Only when an operationj

is assigned to station s,js will be set to one. Otherwise it is set to zero. Similarly, when a workeriis assigned

to machine m, im will be set to one. Dummy variables js are used to ensure appropriate assignments

between operation jand station s whereas im to ensure appropriate assignments between worker iand

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machine m respectively. Furthermore, let aij

be a binary parameter to indicate whether worker ican perform

operationj, that is aij

= 1 if tij

< 2wj

and 0 otherwise. All aijs can be set to unity if one insists that each worker

can perform any task. And also let bjm

be a binary parameter to indicate whether operationjcan be performed

on machine m.

3.1 Traditional Formulation

The assembly line balancing for these sewing operations can be represented as follows.

minimize ii

max (3)

subject to

j,xai

ijij 1 (4)

j,ybm jmjm

= 1 (5)

i,xtj

ijiji = (6)

( )211

21

1 jj,ss

S

ssj

S

ssj

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Fig. 2. Decision variables are all binary variables indicating whether to assign one node to the other

3.2 Heuristic Approach

In order to provide line balancing solution in a reasonable time, the sacrifice on solution's quality must

be made. The greedy strategy is employed in this research. The solution procedure is divided into two

phases. In phase I, operations are assigned to stations based upon standard times. Phase II then assigns all

workers in the team to stations obtained from phase I. It should be noted that by grouping the operations

without considering the workers' limitations in phase I, the solution obtained in the heuristic method cannot

ensure the optimal solution.

Phase I line balancing. This phase involves line balancing formulation with an additional constraint to limit the

number of machines per station and parallel station criteria. In order to allow for parallel stations, a few more

variables are introduced. Suppose there are Sworkers in the team, the average cycle time for the line, Tavg

,

and maximum standard time, Wmax

, can be calculated from standard times wj

of all operations. Then the

maximum number of workers, r, that can be assigned to any station can be calculated from

=

=

jj

jj

avg

max

wS

wmax

T

Wr

1. (12)

Also, let J* be a set of operationsjwith wj[vWmax, Wmax] where vis a value between 0 and 1. The value v

represents criteria for assigning more than one worker to a station, when considering any operation that

belongs to set J*. The value v should be selected according to the distribution of standard times of all

operations necessary to complete the task. Figure 3 denotes an example of histogram of standard time

distribution for a product with maximum standard time of 145 s. and minimum standard time of 24 s. Intuitively

vshould be selected in such a way that all the operations with significantly large standard time be included in

set J*. In most cases vcan be safely set at 0.5

To decompose the problem to smaller sizes, the problem is formulated as an ILP for each station s. The

ILP formulation can be solved progressively from station 1 up to station S. The objective function of this phase

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is to assign operations to each station such that the cycle time at each station, s, is maximized while still not

exceeding the given target cycle time Tc

as shown in constraint (15). Note that if there exists an operationjin

J* included in the station s, i.e.yjs

= 1, the station cycle time is bounded by rTc, else it is bounded by T

c.

maximize s (13)

subject to

==0juj

jsjs yw (14)

cjscjs*Jj

s TyrTymax +

1 (15)

( )21211 jj,yyu sjsjj

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machine m is used in station s. Then the total number of machines used in any station must be less than 3 as

shown in constraint (18). For any given Tc, the number of workers at each station s, q

s, can be calculated from

=c

jjjs

s

T

wy

q (20)

Then the total number of workers required can be calculated by combining the value ofqs

over all stations.

Due to the discrete nature of line balancing problem, Tc

must be varied to identify local optimium. The

searching procedure is assisted by script utility found in many ILP solvers interfacing with Visual Basic

Programming Languages. In this research the lower and upper bounds on Tc

must be be given by the user so

that each integer value ofTc

is explored. Only the one that satisfies the number of worker requirement with

minimal line cycle time is reported. If such value is not found, the program will inform the users to enter

another range ofTc.

Phase II station assignment. The ILP formulation to assign workers to stations can be solved for each team of

workers. First, the time required for each worker ito perform all tasks in station s, Tis

is estimated. This can be

computed from

s,i,tT

jsyjijis =

=

1

(21)

Then the following optimization problem can be solved. Its objective function is to maximize the overall line

cycle time, CT.

minimize CT

(22)

subject to

s,qCTx sTi

isis 2

(23)

s,qx si

is = (24)

i,xs

is = 1 (25)

xis = 0 or 1,

i, s (26)Constraints (23) determine the overall line cycle time. Note that in the case of parallel stations, the cycle

time from these stations must be averaged twice in order to identify the combined station time. Constraints

(24) state that each station must have appropriate number of workers assigned to it whereas constraints (25)

imply that each individual worker must be assigned to a station. It should be noted that the resulting line cycle

time obtained in this phase is different from that obtained in phase I since now the worker's skill are included.

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4. Case Studies

Both optimization phases are implemented on an ILP commercial software, LINGO, interfacing with an

Excel spreadsheet software and Visual Basic Programming Dialog box. An example of product information

from a nylon bag manufacturing company is used to illustrate the solution procedures capability. The

company has several teams of workers to assemble (sew) products. Each team is assigned a product to

assemble every day. Depending on the products order quantity, the team may have to work up to two

products in a day. Table 1 denotes an example of Team 1 workers skill-by-skill evaluation. Note that most

assembly line balancing problems considered by previous works assume that each worker is equally adept to

perform any operations. In practice, this isnt always the case. There are 13 workers in the team. For illustration

purposes, however, let us suppose that worker 10 is absent. The program can skip worker 10 and consider

only the remaining 12 workers available.

In the interest of limited space, the skill evaluation of other teams is omitted here even though such

information can be used in comparing different teams' performance. Two case studies from two different

products are used to illustrate the effects of line balancing parameters. Tables 2 and 3 illustrate product

information used in case studies 1 and 2. The standard time for each operation step, wj, the skill type required

to perform the operation, k, the machine type required to perform such operation, m, and its immediately

preceding operations are also given. The standard time distribution of product 1 is shown in Figure 4.

Table 1. Team 1s skill-by-skill evaluation

skill \ worker 1 2 3 4 5 6 7 8 9 10 11 12 13

1 c a b 0 a 0 0 0 0 : 0 0 0

2 b a a a a b c c c : 0 0 0

3 c b b b a 0 0 0 0 : 0 0 0

4 c c c 0 b 0 a c 0 : 0 0 0

5 a a a a a b b b b : c c 0

6 b a b b a b b b b : c c 0

7 c b a c b 0 0 0 0 : 0 0 0

8 c b b b a c c c a : 0 c 0

: : : : : : : : : : : : : :

49 a a a a a b c c c : 0 c c

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Table 2. Product 1 Specification (12 workers, Tavg

= 252 s.) used for case study 1

j wj

(s.)

k m preceding

operations

j wj

(s.)

k M preceding

operations

1 60 31 5 - 21 116 31 5 20

2 90 36 5 1 22 72 13 3 21

3 60 31 5 2 23 120 34 6 22

4 76 33 5 3 24 51 21 3 23

5 38 16 2 4 25 90 4 8 -

6 18 16 2 5 26 96 32 5 25

7 44 36 5 6 27 36 36 5 26

8 14 42 5 7 28 96 31 5 27

9 36 32 5 8 29 76 27 7 28

10 116 36 5 9 30 38 24 7 29

11 96 33 5 10 31 56 31 5 30

12 103 33 5 11 32 36 32 5 31

13 72 24 5 12 33 36 42 5 32

14 116 27 5 13 34 120 44 4 33

15 116 37 5 14 35 60 32 4 34

16 72 13 3 15 36 24 43 4 35

17 120 34 6 16 37 24 43 4 36

18 51 27 3 17 38 207 35 5 18,24,40

19 28 6 4 - 39 40 45 5 37

20 145 36 5 19 40 51 32 5 38

41 98 21 100 39

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Table 3. Product 2 Specification (12 workers, Tavg

= 103 s.) used for case study 2

j wj

(s.)

k m preceding

operations

j wj

(s.)

k M preceding

operations

1 36 5 4 - 14 48 10 5 13

2 40 45 6 1 15 24 47 3 14

3 51 24 100 2 16 64 3 4 15

4 36 5 5 - 17 36 16 2 16

5 25 45 6 4 18 60 32 6 17

6 32 24 6 5 19 48 31 6 18

7 40 31 6 6 20 48 36 6 -

8 40 38 6 7 21 48 31 6 20

9 48 31 6 8 22 48 27 6 21

10 72 1 5 9 23 30 25 6 22

11 25 31 6 10 24 145 35 5 3,11,19,23

12 42 5 5 - 25 51 16 2 24

13 40 5 5 12 26 64 24 5 25

4.1 Case study 1: maximum standard time is lower than average cycle time

When the maximum standard time, i.e. 207 s., is lower than the average cycle time, 252 s., as shown in

Figure 4, phase I always results in operation grouping with no parallel stations as shown in Table 4. From

systematic search for target cycle time that will yield exact number of workers with locally minimum balance

delay, the target cycle time is found to be 269 s. Variation of the decision criteria, v, to make parallel stations

will not have any effect on the result. The estimated balance delay in phase I is the maximum difference

between target cycle time and estimated station time among all stations, before assigning workers to stations.

For example, in this case, the estimated delay is 269-98 = 171 s. for the line. The last station will have the most

free time of 171 seconds to spare, or 63.5% of target cycle time. This balance delay seems high, but the line

balancing problem considered here is also restricted by the number of machines at each station, making it

difficult to assign workloads more efficiently. When applying phase II, however, the overall line cycle time is

increased to 319.2 s. Table 5 denotes the result of worker assignment to each station.

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Standard Time Distribution

0

1

2

3

4

5

6

7

8

9

10-30 30-50 50-70 70-90 90-110 110-

13 0

130-

15 0

150-

17 0

170-

19 0

190-

21 0

210-

23 0

230-

25 0

250-

27 0

Standard time range

numberofoperations

Tavg = 252 s

Fig. 4. Standard time distribution of all operations required for product 1

Table 4. Result of line balancing in Phase I and Phase II

Phase I Phase II

station operations

performed

station

time(s)

machines

required

number of

workers

worker

assigned

actual station

time (s.)

1 1,2,19,25 268 4,5,8 1 7 250

2 3,4,26,27 268 5 1 3 248.8

3 5-10 266 2,5 1 12 319.2

4 11,28,29 268 5,7 1 4 252.8

5 12,13,30,31 269 5,7 1 2 215.2

6 14,15,32 268 5 1 9 291.2

7 33-37 264 4,5 1 6 223.2

8 20,21 261 5 1 13 313.2

9 16,17,22 264 3,6 1 5 211.2

10 23,24,39,40 262 3,5,6 1 8 286

11 18,38 258 3,5 1 1 226.8

12 41 98 100 1 11 117.6

estimated cycle time 269 total 12 319.2

4.2 Case study 2: maximum standard time is higher than average cycle time

For product 2 with its information as shown in Table 3, it is found that the maximum standard time is

larger than average cycle time. The standard time distribution for this product is as shown in Figure 3. The

decision cretiria for making parallel stations, v, of at least 0.5 will result in target cycle of 115 s. Setting the

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value ofvbelow 0.5 leads to higher target cycle times which is not desired and will not be shown here. Table

5 denotes the result of operation assignment and worker assignment in both Phase I and II. Predicted balance

delay as shown in Phase I is 37.4% due to operation assignment in station 9. After assigning workers to

stations in Phase II, the resulting line cycle time is 129 s. with the balance delay of 55.3%

One may argue whether the methodology of assigning parallel stations is justified as compared to

having only one worker in each station. To investigate such approach, the maximum number of worker per

station, r, is manually set to unity. Using Phase I leads to the use of 9 workers with target cycle time of 145 s.

as shown in Table 6. It should be noted that since the maximum standard time is 145 s., the minimum target

cycle time for the line that can be used is 145 s. After phase II the resulting cycle time yields 144 s. Indeed, 3

remaining workers can work on other assignments as needed. The company should explore the trade-offs

between the cycle time reduction and workers' utilization as the situation calls for.

Table 5. Result of line balancing in Phase I and Phase II (parallel stations allowed)

Phase I Phase II

station operations

performed

station

time(s)

machines

required

number of

workers

worker

assigned

actual station

time (s.)

1 1,4,12 114 4,5 1 4 91.2

2 5,13,20 113 5,6 1 7 113

3 2,14,15 112 3,5,6 1 9 97.6

4 3,16 115 4,100 1 3 115

5 6-8 112 6 1 6 112

6 17,18 96 2,6 1 12 115.2

7 9,21 96 6 1 13 115.2

8 19,22 96 6 1 8 105.6

9 10 72 5 1 2 57.6

10 11,23,24 100 5,6 2 5,11 129

11 25,26 115 2,5 1 1 92

estimated cycle time 115 total 12 129

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Table 6. Result of line balancing in Phase I and Phase II (no parallel station)

Phase I Phase II

station operations

performed

station

time(s)

machines

required

number of

workers

worker

assigned

actual station

time (s.)

1 1,4,5,20 145 4,5,6 1 3 116

2 2,3,21 139 6,100 1 6 131

3 12-14 130 5 1 9 120.9

4 6,7,15,22 144 3,6 1 4 115.2

5 8,16,17 140 2,4,6 1 5 112

6 9-11 145 5,6 1 2 116

7 18,19,23 138 6 1 7 144

8 24 145 5 1 1 116

9 25,26 115 2,5 1 12 138

estimated cycle time 145 total 9 144

6. Conclusion

In this research, a heuristic methodology to perform line balancing with parallel stations is proposed.

The restrictions on the number of machines per station and workers skill level are taken into account. It

consists of two phases. In phase I, operations are grouped into stations such that the target cycle time is not

exceeded, parallel stations are allowed, precedence constraints are satisfied, and the number of machines

per station is limited to 3. It is the most time-consuming stage with locally and manually adjusted step search.

The criteria to make parallel stations depends on the maximum standard time relative to the average cycle

time. As the number of available workers changes, as usually the case in practice, the average cycle time

changes, leading to different line configurations, i.e. machine layouts, operation-station assignment. In phase

II, the stations generated in phase I are assigned to workers in such a way that the overall line cycle time is

minimized. While such greedy approach does not necessarily provide an optimal solution, it is able to

generate a reasonably good solution in short time as compared to traditional line balancing formulation. The

target cycle and the number of workers affect how operations are grouped into stations. The tradeoffs

between cycle time reduction and workforce utilization are necessarily performed by the user. The

comparisons between globally optimal solutions and those provided by this system are necessary and under

way.

Acknowledgement

Author would like to thank the Faculty of Engineering, King Mongkut Institute of Technology North

Bangkok for their partial support in this research.

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